Asymptotic prime divisors of torsion-free symmetric powers of modules

被引：3

作者：

Katz, Daniel ^{[1
]}

Rice, Glenn ^{[2
]}

机构：

[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

[2] Missouri Western State Univ, Dept Comp Sci Math & Phys, St Joseph, MO 64507 USA

来源：

JOURNAL OF ALGEBRA | 2008年 / 319卷 / 05期

关键词：

prime divisor; integral closure; Rees ring; Rees valuation;

D O I：

10.1016/j.jalgebra.2007.10.029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a Noetherian ring, F := R-r and M subset of F a submodule of rank r. Let (A*) over bar (M) denote the stable value of Ass(F-n/M-n), for n large, where Fu is the nth symmetric power of F-n and M, is the image of the nth symmetric power of M in Fn. We provide a number of characterizations for a prime ideal to belong to (A*) over bar (M). We also show that (A*) over bar (M) subset of (A*) over bar (M), where (A*) over bar (M) denotes the stable value of Ass(F-n/M-n). (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：2209 / 2234

页数：26

共 14 条

[1] What is the Rees algebra of a module? [J].